Conventional correlation methods suffer from the slow convergence of electron correlation energies with respect to the size of orbital expansions. This problem is due to the fact that orbital products alone cannot describe the behavior of the exact wave function at short inter-electronic distances. Explicitly correlated methods overcome this basis set problem by including the inter-electronic distances (rij) explicitly in wave function expansions. Here, the origin of the basis set problem of conventional wave function methods is reviewed, and a short history of explicitly correlated methods is presented. The F12 methods are the focus herein, as they are the most practical explicitly correlated methods to date. Moreover, some of the key developments in modern F12 technology, which have significantly improved the efficiency and accuracy of these methods, are also reviewed. In this work, the extension of the perturbative coupled-cluster F12 method, CCSD(T)F12, developed in our group for the treatment of high-spin open-shell molecules (J. Zhang and E. F. Valeev, J. Chem. Theory Comput., 2012, 8, 3175.), is also documented. Its performance is assessed for accurate prediction of chemical reactivity. The reference data include reaction barrier heights, electronic reaction energies, atomization energies, and enthalpies of formation from the following sources: (1) the DBH24/08 database of 22 reaction barriers (Truhlar et al., J. Chem. Theory Comput., 2007, 3, 569.), (2) the HJO12 set of isogyric reaction energies (Helgaker et al., Modern Electronic Structure Theory, Wiley, Chichester, first ed., 2000.), and (3) the HEAT set of atomization energies and heats of formation (Stanton et al., J. Chem. Phys., 2004, 121, 11599.). Two types of analyses were performed, which target the two distinct uses of explicitly correlated CCSD(T) models: as a replacement for the basis-set-extrapolated CCSD(T) in highly accurate composite methods like HEAT and as a distinct model chemistry for standalone applications. Hence, (1) the basis set error of each component of the CCSD(T)F12 contribution to the chemical energy difference in question and (2) the total error of the CCSD(T)F12 model chemistry relative to the benchmark values are analyzed in detail. Two basis set families were utilized in the calculations: the standard aug-cc-p(C)VXZ (X = D, T, Q) basis sets for the conventional correlation methods and the cc-p(C)VXZ-F12 (X = D, T, Q) basis sets of Peterson and co-workers that are specifically designed for explicitly correlated methods. The conclusion is that the performance of the two families for CCSD correlation contributions (which are the only components affected by the explicitly correlated terms in our formulation) are nearly identical with triple- and quadruple-ζ quality basis sets, with some differences at the double-ζ level. Chemical accuracy (~4.18 kJ/mol) for reaction barrier heights, electronic reaction energies, atomization energies, and enthalpies of formation is attained, on average, with the aug-cc-pVDZ, aug-cc-pVTZ, cc- pCVTZ-F12/aug-cc-pCVTZ, and cc-pCVDZ-F12 basis sets, respectively, at the CCSD(T)F12 level of theory. The corresponding mean unsigned errors are 1.72 kJ/ mol, 1.5 kJ/mol, ~ 2 kJ/mol, and 2.17 kJ/mol, and the corresponding maximum unsigned errors are 4.44 kJ/mol, 3.6 kJ/mol, ~ 5 kJ/mol, and 5.75 kJ/mol. In addition to accurate energy calculations, our studies were extended to the computation of molecular properties with the MP2-F12 method, and its performance was assessed for prediction of the electric dipole and quadrupole moments of the BH, CO, H2O, and HF molecules (J. Zhang and E. F. Valeev, in preparation for submission). First, various MP2- F12 contributions to the electric dipole and quadrupole moments were analyzed. It was found that the unrelaxed one-electron density contribution is much larger than the orbital response contribution in the CABS singles correction, while both contributions are important in the MP2 correlation contribution. In contrast, the majority of the F12 correction originates from orbital response effects. In the calculations, the two basis set families, the aug-cc-pVXZ (X = D, T, Q) and cc-pVXZ-F12 (X = D, T, Q) basis sets, were also employed. The two basis set series show noticeably different performances at the double-ζ level, though the difference is smaller at triple- and quadruple-ζ levels. In general, the F12 calculations with the aug-cc- pVXZ series give better results than those with the cc-pVXZ-F12 family. In addition, the contribution of the coupling from the MP2 and F12 corrections was investigated. Although the computational cost of the F12 calculations can be significantly reduced by neglecting the coupling terms, this does increase the errors in most cases. With the MP2-F12C/aug-cc-pVDZ calculations, dipole moments close to the basis set limits can be obtained; the errors are around 0.001 a.u. For quadrupole moments, the MP2-F12C/aug-cc-pVTZ calculations can accurately approximate the MP2 basis set limits (within 0.001 a.u.). / Ph. D.

A novel study on the investigation of three very common atmospheric sulphur species relevant to the Mpumalanga Highveld subregion was conducted. Long-term in situ measurements were applied in the diurnal and seasonal evaluation of the observed sulphur species. Ambient pollutant concentrations and surface meteorological data were collected at an air quality monitoring station at Elandsfontein. Elandsfontein air quality monitoring station was ideal for the observations due to its high elevation within the Mpumalanga Province surrounded by few rolling hills and negligible windbreaks which easily allows for extensive plume-contact with the surface during convective daytime mixing. The temporal characteristics of the sulphur species have been assessed relative to one another with varying meteorological conditions. The diurnal and seasonal concentration variations were used to describe the physical characteristics exhibited by the compounds over Elandsfontein. Pollution roses were used to target the source of the major release points and areas of these sulphur species relative to the Elandsfontein monitoring station. Gas and particle concentrations were analysed in relation to varying meteorological parameters with a view to ascertaining the sulphur transformation and concentration distribution in the planetary boundary layer. Particulate sulphate distribution has been modelled through multivariate regression analyses in relation to three meteorological parameters, namely, wind speed, relative humidity and ambient temperature for the various seasons observed over southern Africa. This study has shown that hydrogen sulphide, sulphur dioxide and sulphate species are present throughout the year in the Mpumalanga Highveld at notably significant levels. The presence of ambient particulate sulphate has been shown to result from the combination of chemical interactions during long-range aerosol transport; atmospheric recirculation processes shown from back trajectories over the southern Africa sub-region, as well as the variation in the removal mechanisms and rates for the different seasons throughout the year. These transport and removal processes all contribute to the overall sulphur mass balance in the planetary boundary layer. Dosage of the three sulphur species was evaluated to provide data for sulphur pollution loading that could form a basis for health and vii environmental impact assessments over the area. In view of the characteristic patterns displayed by particulate sulphate, multivariate mathematical models have been developed on a seasonal basis with variations in meteorological parameters. This was seen to predict an accuracy of up to 70 % of the particulate sulphate loading for different seasons over the South African Highveld. In order to understand the chemical interactions of atmospheric sulphur species, it is important to be able to predict the route taken and expected products of transformation on any given condition. Theoretical analyses of the chemical thermodynamic properties of the known reacting species and a well-established approach were used in predicting reaction paths and establishing the possible and feasible products of chemical transformation in relation to the ambient temperature. The determination of reaction paths and possible products of chemical transformation provides a measure of the relative importance of the reacting species and the mechanism of reaction. Gas-, aqueous-phase and radical reactions involving sulphur (IV) were investigated with a view to establishing their relative importances. Thermochemical properties of several sulphur-containing compounds not available in the literature have been generated for evaluation of Gibbs free energy (ΔG) and enthalpy (ΔH). An electronic energy structural approach has been applied to model for ΔG and ΔH of 88 sulphur species in 90 chemical reactions comprising gas-phase, aqueousphase and radical reactions. Modelling was evaluated for their relative importances over a temperature range of –100 °C to +100 °C. The temperature range is well above the known tropospheric temperature range to account for variations in the atmospheric environment. To further comprehend the chemistry of sulphur with regards to distribution of the species in the atmosphere, a kinetic model is developed and incorporated into a dispersion model. The kinetic evaluation of the oxidation rate of SO2 to sulphate has been determined with advection and dispersion over the Elandsfontein area. Gas-phase transformation with advection and dispersion has been used to evaluate the extent of the distribution of SO2 relative to the major contributing sources. The dry deposition was considered to be the dominant removal mechanism. It was assumed that the reaction rate was second order in concentration and that the rate of deposition was first order. The oxidation rates obtained for the seasons were 10.9 % h-1 for summer; 8.83 % h-1 for autumn; 6.56 % h-1 for winter; viii 10.8 % h-1 for spring, while an overall rate of 9.6 % h-1 was obtained for the one year study period. The transformation rate model produced a reaction constant and an activation energy of 4.92 x 10-6 μg m-3 s-1 and 36.54 kJ kg-1 for summer; 3.939 x 10-6 μg m-3 s-1 and 43.89 kJ kg-1 for autumn; 2.90 x 10-6 μg m-3 s-1 and 115.69 kJ kg-1 for winter; 4.82 x 10-6 μg m-3 s-1 and 43.29 kJ kg-1 for spring, while for the year 4.29 x 10-6 μg m-3 s-1 and 34.31 kJ kg-1. A Gaussian puff unsteady state Lagrangian dispersion model with reflection at the surface and inversion layer was applied for concentration diffusion. The Lagrangian dispersion model with dry deposition was a better prediction of the observed data than the models from previous studies using a first order rate constant with or without deposition rate.